The secure key length, \(\ell \) , is calculated using Eqs. (REF ), (REF ) and (REF ), together with Eqs. (1) to (5) from [1]}. The extraneous count probability, \(p_{ec}\) , and the intrinsic quantum bit error rate, \(QBER_I\) , induce the errors, which in turn affects \(\ell \) . We detail the relationship in this appendix. The approach is the same as outlined in [2]}.
